List of top Questions asked in MHT CET

A parallel plate capacitor having capacity \(12\) pF is charged by a battery of \(10\) V between its plates. The battery is now disconnected and a slab of dielectric constant \(6\) is kept between the plates. The work done by the capacitor on the slab is

A parallel plate air capacitor has capacity \(C\) and plate area \(A\). Now the space between its plates is filled by two slabs of thickness \(\frac{d}{2}\) each, having dielectric constants \(K_{1}\) and \(K_{2}\). Distance of separation between plates is \(d\). The capacity of the capacitor is (\(\varepsilon _{0}\) = permittivity of free space)

\(n_{1}\) is the fundamental frequency of the pipe closed at one end and \(n_{2}\) is the fundamental frequency of the pipe open at both ends. If both are joined end to end, the fundamental frequency of closed pipe so formed is

A mass is suspended from a vertical spring which is executing S.H.M. of frequency \(10\) Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is (\(g=10\text{m/s}^{2}\))

The path length of oscillation of simple pendulum of \(1\) m is \(8\) cm. Its maximum velocity is (Take \(g=\pi ^{2}\text{m/s}^{2}\))

Maximum kinetic energy of a particle of mass \(1\) kg in S.H.M. is \(8\) J and the time period is \(4\) s. Maximum potential energy during the motion is \(10\) J. Then

Two uniform strings A and B made of steel are vibrating under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is

An observer moves towards a stationary source of sound with a velocity \(\left(\frac{1}{5}\right)^{th}\) of the velocity of sound. The percentage increase in the apparent frequency is

\(1\) g of water of volume \(1\text{cm}^{3}\) at \(100^{\circ }\text{C}\) is converted into steam of same temperature under normal atmospheric pressure (\(10^{5}\) Pa). The volume of steam formed equals \(1671\text{cm}^{3}\). If the latent heat of vaporisation of water is \(2256\) J/g, the change in internal energy is

The wavelength of maximum intensity of radiation emitted by a star is \(289.8\) nm. The radiation intensity of the star is (Stefan's constant = \(5.67\times 10^{-8}\) SI unit, Wein's constant \(2898\mu \text{mk}\))

The temperature of an ideal gas increases \(2\) times when compressed adiabatically to half the volume. Its equation of state is

At \(10^{\circ }\text{C}\), the value of density of a fixed mass of a gas (ideal) divided by its pressure is \(x\). At \(110^{\circ }\text{C}\) this ratio is

At \(273^{\circ }\text{C}\), the emissive power of a perfectly black body is \(R\). The value at \(0^{\circ }\text{C}\) is

The coefficient of volume expansion of mercury is \(18\times 10^{-5}/^{\circ }\text{C}\). A thermometer bulb has volume \(10^{-6}\text{m}^{3}\) and cross-section of stem is \(0.004\text{cm}^{2}\). Assuming bulb is filled with mercury at \(0^{\circ }\text{C}\) then the mercury column at \(100^{\circ }\text{C}\) is

The moment of inertia of a solid sphere about an axis passing through centre of gravity is \(\frac{2MR^{2}}{5}\) where M is the mass and R is the radius. The radius of gyration about a parallel axis at a distance \(2R\) from first axis is

Two particles of masses \(m\) and \(M\) are placed a distance \(d\) apart. The gravitational potential at the position where the gravitational field due to them is zero is \(V\). Then

A drop of some liquid of volume \(0.04\text{cm}^{3}\) is placed on the surface of the glass plate. Then another glass plate is placed on it such that the liquid forms a thin layer of area \(20\text{cm}^{2}\) between the surfaces. To separate the plates a force of \(16\times 10^{5}\) dyne has to be applied normal to the surfaces.
The surface tension of the liquid in dyne/cm is

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio \(16:9\). The ratio of their surface area is

Water rises up to a height \(h\) in a capillary tube on the surface of the earth. The value of \(h\) will increase, if the experimental set up is kept in (\(g\) = acceleration due to gravity)

A particle of mass \(m\) is projected with speed \(v\) at \(45^{\circ }\) with the horizontal. The magnitude of angular momentum of the particle about the point of projection when the particle is at its maximum height \(h\) is \(\left(\cos 45^{\circ }=\frac{1}{\sqrt{2}}\right)\)

A stone is thrown at an angle \(\theta\) with the horizontal reaches a maximum height \(H\), then the time of flight of stone will be (\(g\) = acceleration due to gravity)

If the error in the measurement of volume of the sphere is \(6\%\) then the error in the measurement of its surface area will be

A bullet is fired from a gun. The force on the bullet is \(F=(600-2\times 10^{5}t)\) N where \(t\) is in second. The force on the bullet becomes zero as soon as it leaves the barrel. The average impulse imparted to the bullet is

A disc of moment of inertia \(I_{1}\) is rotating in horizontal plane about an axis passing through centre and perpendicular to its plane with constant angular speed \(\omega _{1}\). Another disc of moment of inertia \(I_{2}\) having zero angular speed is placed co-axially on a rotating disc. Now, both the discs are rotating with constant angular speed \(\omega _{2}\). The energy lost by the entire system is \(\frac{x\omega _{1}^{2}}{2}\) where the value of \(x\) is

A vector \(\vec{A}\) has magnitude \(6\) units is added to vector \(\vec{B}\) which is along \(x\)-axis. The resultant of \(\vec{A}\) and \(\vec{B}\) is along \(y\)-axis. If the magnitude of the resultant of \(\vec{A}\) and \(\vec{B}\) is \(3\) times that of \(\vec{B}\) then the magnitude of \(\vec{B}\) is